As already explained in the Introduction, the homogeneous case of
constant \(\xi \)  has been well-understood by now (and, in fact, to a much
finer extent than illustrated in the Introduction, see e.g. [1]} and references therein for further details). Also the
heterogeneous case of random non-linearities we are dealing with has been
investigated before. Specifically, under fairly general assumptions, the
existence and characterization of the propagation speed (i.e., the linear
order of the position of the front
\(\lim _{t \rightarrow \infty } m^\varepsilon (t)/t\) ) have been derived by
Freidlin and Gärtner, see e.g. [2]} as well as
[3]} using large deviation principles. Incidentally,
the Feynman-Kac formula (see also Section REF  below), which
characterizes the solution to the linearization (REF ), also
played an important role in the derivation.
